Lab 5 RS

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LC Resonance circuits

The LC cicuit

1. Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]L[/math] = 10 - 100 [math]\mu H[/math].

[math]\omega_0=\frac{1}{\sqrt{\mbox{LC}}}[/math]

1. Construct the LC circuit using a non-polar capacitor
2. Measure the Gain [math]\equiv \frac{V_{out}}{V_{in}}[/math] as a function of frequency. (20 pnts)
3. Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke [math]R_{L}[/math]. (20 pnts)
4. Compare the measured and theoretical values from the resonance frequency ([math]\omega_{L}[/math]) and the Quality factor [math]Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}}[/math] value for each case; [math]W = \frac{1}{2}LI^2[/math]. (10 pnts)

Questions

1. If r=0, show that [math]Q = \frac{1}{\omega_0 R_L C}[/math]. (10 pnts)
2. Show that at resonance[math] Z_{AB} \approx Q \omega_0 L[/math]. (10 pnts)

The LRC cicuit

1. Design and construct a series LRC circuit.
2. Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 pnts)

Questions

1. What is the current [math]I[/math] at resonance? (5 pnts)
2. What is the current as [math]\nu \rightarrow \infty[/math]? (5 pnts)

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